UC Berkeley

This work furthers the program of understanding the black hole information paradox, the firewall paradox, and the relevance of concepts from quantum information to quantum gravity. A gravitational calculation was recently shown to yield the Page curve for the entropy of Hawking radiation. In this work, we generalize the Ryu-Takayanagi (Quantum Extremal Surface) prescription for von Neumann entropies to various settings relevant for this calculation. We examine a puzzle in the calculation, which we call the state paradox: that the calculation makes use of Hawking's result that the radiation entropy becomes large at late times. The paradox is resolved if the gravitational path integral computes averaged quantities in a suitable ensemble of unitary theories. We apply the insights from these calculations to cosmology by searching for entanglement islands in cosmologies with spatial curvature containing thermal radiation purified by a reference spacetime. We show arbitrarily small positive curvature guarantees that the entire universe is an island. Proper subsets of the time-symmetric slice of a closed or open universe can be islands, but only if the cosmological constant is negative and sufficiently large in magnitude. We extend this analysis to cosmologies containing a general fluid, finding that flat universes with time-symmetric slices always have islands on that slice. We find islands in the Simple Harmonic Universe model, which has no classical singularity at the background level. We then argue that the Page curve calculations do not resolve the firewall paradox. We exhibit a sharpened version of the paradox which consists of the Hayden-Preskill thought experiment in which the message thrown into the black hole is itself a smaller black hole. We argue that accounting for decoherence resolves the paradox. Finally, we conclude with an argument that quantum complexity theory can quantify the difficulty of distinguishing eigenstates obeying the Eigenstate Thermalization Hypothesis (ETH).